\documentclass{article}

\usepackage{../../util}

\title{Vectors and Matrices}
\author{Cambridge University Mathematical Tripos: Part IA}

\begin{document}
\maketitle

\tableofcontentsnewpage{}

\section{Complex numbers}
\input{01_complex_numbers.tex}
\section{Vectors in three dimensions}
\input{02_vectors_in_three_dimensions.tex}
\section{Index notation and the summation convention}
\input{04_index_notation_and_the_summation_convention.tex}
\section{Higher dimensional vectors}
\input{05_vectors_in_real_euclidean_space.tex}
\section{Linear maps}
\input{08_linear_maps.tex}
\section{Transpose and Hermitian conjugate}
\input{09_transpose_and_hermitian_conjugate.tex}
\section{Adjugates and alternating forms}
\input{10_adjugates_and_alternating_forms.tex}
\section{Determinant}
\input{11_determinant.tex}
\section{Properties of matrices}
\input{13_eigenvalues_and_eigenvectors.tex}
\section{Quadratic forms}
\input{16_quadratic_forms.tex}
\section{Cayley--Hamilton theorem}
\input{17_cayley_hamilton_theorem.tex}
\section{Changing bases}
\input{18_changing_bases.tex}
\section{Conics and quadrics}
\input{19_conics_and_quadrics.tex}
\section{Symmetries and transformation groups}
\input{20_symmetries_and_transformation_groups.tex}

\end{document}
